Installing and upgrading help

I would keep lang as this contains all modifications to the language packs (it is still stored in DB also but wouldn't activate until the language packs are saved again).

Models contains data for the Analytics - I would keep this if you're actively using this feature.

MUC can be left as this will be re-created on the site initial load.

Temp can be left also.

+1 to what Jamie said ... cept thought temp was just that and not something one would really need restoring or transferring a site.

One way to find out for sure ... go to moodledata and hide a directory ... like MUC ... mv muc .muc ... see the 'dot' in front of the second 'muc'?   That hides ... then run a cli cron a couple of times, hit site and login as admin, click around.   Is muc rebuilt?   Then not needed in archive for restoring or transfer to another server.

Do same with other directories you've asked about.

Yes, pain in the ... but don't think there are any docs that addresses what directories are absolutely needed on restore/transfer ... could have missed it, however ... we know that filedir is.

If something hickups, then one can put the muc directory back by reversing the mv command.

Am curious about issues with rsync.   Mind sharing?   Reason I ask, have been using rsync for backups of very large moodle site filedir's.

'spirit of sharing', Ken

At a pinch, yes. Your site will still function.